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Title:
Planar flows: from graphene to planet atmospheres
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Abstract:
Fluid mechanics in two dimensions has wide range of applications and possesses unique mathematical properties which are far from being fully explored. Even laminar and regular flows in two dimensions are of great interest ranging from microfluidics to emerging viscous electronics in graphene and other strongly interacting systems. They possess such remarkable features as negative resistance and super-ballistic conductance. On the other hand, a landmark feature of turbulence in two dimensions is an inverse cascade, that is an appearance of large vortices and jets out of multi-scale random flow. It is the most significant and most surprising discovery in turbulence in the last fifty years. We still have no adequate conceptual framework for this counter-intuitive process of self-organization. Several inverse cascades demonstrate conformal invariance, found empirically and still having no theoretical explanation. After the inverse cascade reaches the system size, it creates a coherent flow called condensate. Interaction of turbulence and condensate is presently one of the most active fields of turbulence research. Apart from fundamental importance, inverse turbulence cascades and condensates are ubiquitous features of astrophysical, geophysical and industrial flows, from planet atmospheres to tokamak plasma. This colloquium will give an elementary presentation of physical phenomena ranging from current vortices in graphene to jets and vortices in planet atmospheres
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